The present invention relates generally to corrugating machines and, more particularly, to improvements in single-facer and double-facer units of the corrugating machines. The single-facer unit includes an adhesive applicator roller having an engraved surface that transfers or "prints" transverse parallel rows of adhesive onto a first liner, and means to contact said rows of adhesive with and bond said liner to the corrugation peaks of a corrugated medium to form a single-faced corrugated web; and the double-facer unit includes mechanism that maintain a single-face web in engagement for a predetermined interval with an adhesive applicator roller having a uniformly engraved surface which transfers or "prints" adhesive to the exposed corrugation peaks of the single-face web, and includes mechanisms to contact and bond the single-face web to a second liner to form a double-face corrugated web. The invention can also be used to form multi-ply corrugated structures, as well as to combine heat-sensitive, non-porous or highly graphic materials, the use of which was impractical under prior art methods.